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Question

# We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, ∠ ABC = 110∘, ∠ DAC = 15∘, ∠ CAB=25∘, AB = 5cm, CD = 7cm. Can we construct this parallelogram?

A

Yes, of course

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B

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C

With AC, yes

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D

No, it is impossible

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Solution

## The correct option is D No, it is impossible Step1: Draw rough diagram of the parallelogram ABCD Here, ∠ DAC = ∠ ACB= 15∘ - (1) (Alternate interior angles) In △ ABC, ∠ A + ∠ B + ∠ C must be 180∘ ∠ A + ∠ B + ∠ C = 25∘ + 110∘ + 15∘ (from (1)) ∠ A + ∠ B + ∠ C = 150∘ The sum of angles in a triangle should always be equal to 180∘. So, this construction is not possible.

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